1.
6.
Find the next number in the pattern 30, 32, 36, 42, 50, ___.
Explanation
The pattern in this sequence involves adding consecutive prime numbers. Starting with 30, the next prime number is 31, so 30 + 31 = 61. Therefore, the next number in the pattern is 61.
2.
ESSAY: Chapter1 The Fencing Problem - Math The task A farmer has exactly 1000m of fencing; with it she wishes to fence off a level area of land. She is not concerned about the shape of the plot but it must have perimeter of 1000m. What she does wish to do is to fence off the plot of land which contains the maximun area. Investigate the shape/s of the plot of land that have the maximum area.
3.
1.
The volume of a box is found by multiplying its height h, length l, and width w. If the measure of the volume of a box is 130, what could its dimensions be?
Correct Answer
C. 2 by 5 by 13
Explanation
The volume of a box is calculated by multiplying its height, length, and width. In this case, the volume is given as 130. Among the given options, the only set of dimensions that satisfies this condition is 2 by 5 by 13. If we multiply these dimensions (2 x 5 x 13), we get a volume of 130. Therefore, the correct answer is 2 by 5 by 13.
4.
2.Find the area of the square.
Correct Answer
D. 49 in2
Explanation
The answer 49 in2 is correct because the formula to find the area of a square is side length squared. In this case, the side length of the square is 7 inches (since 7 x 7 = 49), so the area is 49 square inches.
5.
3.The Ming dynasty in China ended in the year 1644. It had lasted for 276 years. In what year did the Ming dynasty begin?
Correct Answer
A. 1368
Explanation
The Ming dynasty in China began in the year 1368. This can be inferred from the information given that the dynasty lasted for 276 years and ended in 1644. By subtracting 276 years from 1644, we get the starting year of the Ming dynasty as 1368.
6.
4.In 1999, the state of Vermont produced 60,000 more gallons of maple syrup than Michigan, Ohio, Pennsylvania, and Wisconsin combined. Use the table to find how many gallons of maple syrup Vermont produced in 1999.
Correct Answer
B. 370,000
Explanation
Based on the information given, Vermont produced 60,000 more gallons of maple syrup than the combined total of Michigan, Ohio, Pennsylvania, and Wisconsin. Since the exact combined total is not provided, we cannot determine the individual production of each state. Therefore, the only information we have is that Vermont produced 60,000 more gallons than the combined total. So, the amount produced by Vermont must be higher than the highest possible combined total, which is 310,000 gallons. Therefore, the answer is 370,000 gallons.
7.
5.The Rodriguez family is taking a vacation that costs $1,400. They are making a down payment of $500 and paying the rest in three equal payments. What will be the amount of each payment?
Correct Answer
D. $300
Explanation
The Rodriguez family is making a down payment of $500, which means they have to pay the remaining amount of $1,400 - $500 = $900. Since they are paying this amount in three equal payments, each payment will be $900 / 3 = $300.
8.
7.Solve 16 = k + 10 using mental math.
Correct Answer
D. 6
Explanation
To solve the equation 16 = k + 10 mentally, we can start by subtracting 10 from both sides of the equation. This gives us 6 = k. Therefore, the value of k that satisfies the equation is 6.
9.
8. Which rule describes how to find the next number in the pattern–5, -1, 3, 7?
Correct Answer
Add 4
add 4
ADD 4
Explanation
The rule for finding the next number in the pattern is to add 4 to the previous number. This is evident from the sequence -5 + 4 = -1, -1 + 4 = 3, and 3 + 4 = 7. The pattern follows a consistent increase of 4 with each step.
10.
9.What are the rules for the order of operations?
Correct Answer
D. Multiply and divide in order from left to right. Then add or subtract in order from left to right.
Explanation
The rules for the order of operations state that you should first perform any multiplication or division operations from left to right, and then perform any addition or subtraction operations from left to right. This ensures that the calculations are done in the correct order and that the correct result is obtained.
11.
10.The cost of admission to a science museum is 12a + 5c, where a represents the number of adults and c represents the number of children. How much would it cost for 2 adults and 3 children to go to the museum?
Correct Answer
C. $39
Explanation
The cost of admission to the science museum is given by the expression 12a + 5c, where a represents the number of adults and c represents the number of children. In this case, there are 2 adults and 3 children, so we can substitute a = 2 and c = 3 into the expression. Therefore, the cost would be 12(2) + 5(3) = 24 + 15 = $39.
12.
11. Evaluate 2xy + 9 if x = 3 and y = 2.
Correct Answer
B. 21
Explanation
To evaluate the expression 2xy + 9, we substitute the given values of x = 3 and y = 2 into the expression. So, we have 2(3)(2) + 9. Simplifying this, we get 12 + 9, which equals 21. Therefore, the correct answer is 21.
13.
12. Find the missing output values for the function table.
Correct Answer
C. 1, 3, 5
Explanation
The missing output values for the function table can be found by observing the pattern in the given values. In the first row, the output values increase by 2 each time. In the second row, the output values increase by 2 each time. In the third row, the output values increase by 2 each time. Therefore, following the same pattern, the missing output values for the fourth row would be 1, 2, 3.
14.
13.For each job, an automobile technician charges $50 per hour for labor. Define a variable. Then write a function rule that relates the total charge for labor to the number of hours of labor.
Correct Answer
D. 50h
Explanation
The correct answer is 50h. This is because the function rule is stating that the total charge for labor is equal to the number of hours of labor multiplied by the rate of $50 per hour. Therefore, the variable h represents the number of hours of labor and multiplying it by 50 gives the total charge for labor.
15.
14.Find the rule for the function table.
Correct Answer
C. N-5
Explanation
The rule for the function table is to subtract 5 from the given value of n.
16.
15.NUMBERS Lucy has chosen three numbers from 1 through 9 whose product is 36. Find the numbers.
Correct Answer
B. 2, 3, and 6
Explanation
The three numbers chosen by Lucy have a product of 36. The only combination of three numbers from 1 through 9 that multiplies to 36 is 2, 3, and 6.
17.
16.LUNCH Jenna’s mother bought lunch for her and her three friends. The restaurant offered a hamburger combo meal for $3.75 and a chicken sandwich combo meal for $4.25. If the total for lunch was $16.50, how many of each combo meal did they order?
Correct Answer
C. 1 hamburger combo and 3 chicken sandwich combos
Explanation
Jenna and her three friends ordered a total of four combo meals for lunch. Since the total cost of lunch was $16.50, and the cost of a hamburger combo is $3.75, the cost of the hamburger combos would be 1 * $3.75 = $3.75. The remaining cost of $16.50 - $3.75 = $12.75 would be the cost of the chicken sandwich combos. Since the cost of a chicken sandwich combo is $4.25, the number of chicken sandwich combos would be $12.75 / $4.25 = 3. Therefore, they ordered 1 hamburger combo and 3 chicken sandwich combos.
18.
17.
The rectangles show that the number 23 ______.
Correct Answer
B. Is prime
Explanation
The rectangles show that the number 23 is prime. This is because a prime number only has two factors, 1 and itself. The rectangles indicate that there are only two factors for the number 23, confirming that it is prime.
19.
18.Find the prime factorization of 105.
Correct Answer
C. 3 × 5 × 7
Explanation
The prime factorization of 105 is 3 × 5 × 7. This means that 105 can be expressed as the product of these prime numbers.
20.
19.Find 213 ÷ 3.
Correct Answer
C. 71
Explanation
To find the quotient of 213 divided by 3, we divide 213 by 3. When we do this, we get 71. Therefore, the correct answer is 71.
21.
20.What is the area of the top of a cubic ice cube with sides of length 2 cm?
Correct Answer
B. 4 cm2
Explanation
The area of the top of a cubic ice cube can be found by squaring the length of one side. In this case, the sides of the ice cube are 2 cm long, so the area of the top is 2 cm x 2 cm = 4 cm2.
22.
21.Your parents tell you that they will give you a weekly allowance of $2 every time you do the dishes, $5 every time you sweep the floor, and $3 every time you pull weeds. How much money will you get if you do the dishes three times, sweep the floor once, and pull weeds twice in a week?
Correct Answer
D. $17
Explanation
If you do the dishes three times, you will earn $2 x 3 = $6. If you sweep the floor once, you will earn $5. And if you pull weeds twice, you will earn $3 x 2 = $6. Therefore, the total amount of money you will get is $6 + $5 + $6 = $17.
23.
22.Evaluate 6 · 7 – 2p if p = 5.
Correct Answer
D. 32
Explanation
To evaluate the expression 6 · 7 - 2p, we substitute p with 5 since it is given. This gives us 6 · 7 - 2(5). Simplifying further, we have 42 - 10, which equals 32. Therefore, the correct answer is 32.
24.
23.You're playing a car racing video game and have 52 points. You get 30 more points for coming in third place and then your score is doubled for having a total time under two minutes. What is your final score?
Correct Answer
A. 164 points
Explanation
In the car racing video game, the player starts with 52 points. By coming in third place, they earn an additional 30 points, bringing their total to 82 points. Then, their score is doubled for completing the race in under two minutes. Doubling 82 gives a final score of 164 points.
25.
24.Evaluate x^{3} if x = 7.
Correct Answer
A. 343
Explanation
When evaluating x^3, we need to substitute the value of x, which is 7, into the expression. Therefore, 7^3 equals 343.
26.
25.The measurements of two different rectangular swimming pools are 35 feet by 13 feet and 41 feet by 12 feet. What is the difference in their areas?
Correct Answer
C. 37 square feet
Explanation
The difference in the areas of the two rectangular swimming pools can be found by subtracting the area of the smaller pool from the area of the larger pool. The area of a rectangle is calculated by multiplying its length by its width. Therefore, the area of the first pool is 35 feet * 13 feet = 455 square feet, and the area of the second pool is 41 feet * 12 feet = 492 square feet. Subtracting the smaller area from the larger area, we get 492 square feet - 455 square feet = 37 square feet.
27.
26.GROCERIES A family purchased milk and bread at the grocery store. Each gallon of milk cost $2.75, and each loaf of bread cost $1.50. If the family spent a total of $10 on 5 items, how many of each did they buy?
Correct Answer
D. 2 gallons of milk and 3 loaves of bread
Explanation
The family spent a total of $10 on 5 items. Let's assume they bought x gallons of milk and y loaves of bread. Each gallon of milk costs $2.75 and each loaf of bread costs $1.50. So, the equation can be set up as 2.75x + 1.50y = 10.
To find the values of x and y, we can solve this equation. By trying out the given options, we find that when x = 2 and y = 3, the equation is satisfied: 2.75(2) + 1.50(3) = 5.50 + 4.50 = 10.
Therefore, the family bought 2 gallons of milk and 3 loaves of bread.
28.
27.One of Macario’s notebooks measures 11 inches by 10 inches. His other notebook measures 8 inches by 10 inches. What is the difference in the areas of the front covers of the notebooks?
Correct Answer
B. 30 square inches
Explanation
The difference in the areas of the front covers of the notebooks can be found by subtracting the area of the smaller notebook from the area of the larger notebook. The area of a rectangle can be calculated by multiplying its length by its width. Therefore, the area of the larger notebook is 11 inches * 10 inches = 110 square inches, and the area of the smaller notebook is 8 inches * 10 inches = 80 square inches. Subtracting the area of the smaller notebook from the area of the larger notebook gives us 110 square inches - 80 square inches = 30 square inches.
29.
28.A high school regulation basketball court measures 50 feet wide and 84 feet long. A junior high school basketball court measures 42 feet wide and 74 feet long. How much smaller is a junior high school basketball court than a high school basketball court?
Correct Answer
B. 1,092 square feet
Explanation
A junior high school basketball court is smaller than a high school basketball court by 1,092 square feet. This can be calculated by finding the difference in the areas of the two courts. The area of the high school court is 50 feet wide multiplied by 84 feet long, which equals 4,200 square feet. The area of the junior high school court is 42 feet wide multiplied by 74 feet long, which equals 3,108 square feet. Subtracting the area of the junior high school court from the area of the high school court gives us a difference of 1,092 square feet.
30.
29.CATALOGS Michelle ordered T-shirts and tank tops from a catalog. Each T-shirt cost $12, and each tank top cost $8. If her total, without tax and shipping, was $56 for 6 items, how many of each did she order?
Correct Answer
D. 2 T-shirts and 4 tank tops
Explanation
Michelle ordered 2 T-shirts and 4 tank tops. To find the answer, we can set up a system of equations. Let's represent the number of T-shirts as "x" and the number of tank tops as "y". From the given information, we know that the cost of each T-shirt is $12 and the cost of each tank top is $8. So, the total cost can be expressed as 12x + 8y. We also know that the total cost of 6 items is $56, so we can set up the equation 12x + 8y = 56. To solve this equation, we can use substitution or elimination method. By solving the equation, we find that x = 2 and y = 4, which means Michelle ordered 2 T-shirts and 4 tank tops.
31.
30.ORDER OF OPERATIONS Use the symbols +, −, ×, or ÷ to make the following sentence true. Use each symbol only once.
5 □ 2 □ 6 □ 1 = 16
Correct Answer
D. 5 + 2 × 6 − 1 = 16
Explanation
The correct answer is 5 + 2 × 6 − 1 = 16. This is because according to the order of operations, multiplication and division should be performed before addition and subtraction. So, first, we multiply 2 and 6 which gives us 12. Then, we add 5 to 12 which gives us 17. Finally, we subtract 1 from 17 which gives us 16.
32.
31.MONEY Joe has 7 bills in his wallet that total $20. What are the bills?
Correct Answer
B. One $10 bill, one $5 bill, and five $1 bills
Explanation
Joe has a total of 7 bills in his wallet. The bills need to add up to a total of $20. The combination that satisfies this condition is one $10 bill, one $5 bill, and five $1 bills. This combination adds up to $10 + $5 + (5 x $1) = $20.
33.
32.
For each job, an automobile technician charges $50 per hour for labor. Define a variable. Then write a function rule that relates the total charge for labor to the number of hours of labor.
Correct Answer
D. 50h
Explanation
The correct answer is 50h. This is because the function rule that relates the total charge for labor to the number of hours of labor is given by multiplying the number of hours (h) by the charge per hour ($50). Therefore, the total charge for labor can be represented as 50h.